{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import seaborn\n",
    "seaborn.set_style(\"whitegrid\")\n",
    "\n",
    "from scipy.optimize import brentq, minimize_scalar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "update_figs = True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from procedures import dh, FindEffort\n",
    "from procedures import FindSWF2, Find_p_opt2, FindSCPE2, CalibrateModel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "M = [(0.625/0.525)**2, # ratio of variance of log earnings, pp over fp, LMP Figure 5\n",
    "     1,                # share of excess variance explained by bonuses\n",
    "     1.576,            # ratio of mean earnings at two job types, self-calculated following LMP\n",
    "     0.618]            # total variance of log earnings, HT\n",
    "\n",
    "ε = 0.5\n",
    "\n",
    "p_emp = 0.181 # Heathcote Storesletten Violante (2017)\n",
    "\n",
    "### From Heathcote and Tsujiyama (2019)\n",
    "λ_θ = 2.2\n",
    "Y_emp = 77.325 # mean household labor income in 1,000$\n",
    "g_emp = 0.188 # G/Y\n",
    "G_emp = g_emp * Y_emp\n",
    "\n",
    "### From Lemieux MacLeod and Parent (2009)\n",
    "s_pp = 0.45 # share of pp jobs, Figure 4\n",
    "\n",
    "# Calculate the probability of receiving a bonus (based on Table II, focus on 90s)\n",
    "# share_b: share of bonuses-pay jobs in all performance-pay jobs \n",
    "# (adjusting for a number of times the job match was observed)\n",
    "share_b = (30.24 + 6.31)/(37.56 + 7.06)\n",
    "prob_b = (0.37 + share_b - 1)/share_b\n",
    "π = np.round(prob_b, decimals=2)\n",
    "\n",
    "params = CalibrateModel(M, π, ε, s_pp, λ_θ, p_emp, Y_emp, G_emp)\n",
    "ε_pp, h̄_pp = params[3], params[4]\n",
    "σ2_pp, μ_pp, σ2_fp, μ_fp = params[7:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Optimal policy exercise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 648x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pV = np.linspace(0, 0.7, 100)\n",
    "SWF = [FindSWF2(p, *params) for p in pV]\n",
    "\n",
    "p_opt = Find_p_opt2(*params)\n",
    "SWF_opt = FindSWF2(p_opt, *params)\n",
    "\n",
    "p_SCPE = FindSCPE2(*params)\n",
    "SWF_SCPE = FindSWF2(p_SCPE, *params)\n",
    "\n",
    "SWF_status_quo = FindSWF2(p_emp, *params)\n",
    "\n",
    "\n",
    "def cons_eq(x, reference=SWF_status_quo):\n",
    "    \"\"\"Translate into consumption equivalent relative to the reference level of SWF\"\"\"\n",
    "    return np.exp(x - reference) - 1\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(9, 5))\n",
    "fs = 20\n",
    "fs2 = 20\n",
    "\n",
    "plt.plot(pV, cons_eq(SWF), 'k', lw=3, label=\"SWF in the calibrated model\")\n",
    "plt.plot(p_opt, cons_eq(SWF_opt), marker='o', color='k', markersize=14)\n",
    "textC = \"optimum: p = \" + str(np.round(p_opt, decimals=2)) \n",
    "textC = textC + \"\\nwelfare change: \" + str(np.around(100*cons_eq(SWF_opt), decimals=2)) + \"%\" \n",
    "ax.annotate(textC, (p_opt, cons_eq(SWF_opt)), \n",
    "            xytext=(p_opt-0.16, cons_eq(SWF_opt) + 0.005), color=\"k\", size=fs2)\n",
    "\n",
    "ax.plot(p_SCPE, cons_eq(SWF_SCPE), marker='o', color='k', linestyle=\"none\", markersize=14)\n",
    "textSCPE = \"SCPE: p = \" + str(np.around(p_SCPE, decimals=2)) \n",
    "textSCPE = textSCPE + \"\\nwelfare change: \" + str(np.around(100*cons_eq(SWF_SCPE), decimals=2)) + \"%\" \n",
    "ax.annotate(textSCPE, (p_SCPE, cons_eq(SWF_SCPE)), \n",
    "            xytext=(p_SCPE + 0.01, cons_eq(SWF_SCPE)), color=\"k\", size=fs2)\n",
    "\n",
    "ax.plot(p_emp, 0, marker='o', color='black', linestyle=\"none\", markersize=14)\n",
    "text_status_quo = \"status quo\\n p = \" + str(np.around(p_emp, decimals=3)) \n",
    "ax.annotate(text_status_quo, (p_emp, 0), \n",
    "            xytext=(p_emp - 0.07, 0.006), color=\"black\", size=fs2)\n",
    "\n",
    "ax.set_xlim([0.1, 0.6])\n",
    "xticksv = np.linspace(0.1, 0.6, 6)\n",
    "ax.set_xticks(xticksv)\n",
    "ax.set_xticklabels([str(np.round(x, decimals=1)) for x in xticksv], fontsize=fs-2)\n",
    "ax.set_xlabel('progressivity rate $p$', fontsize=fs)\n",
    "\n",
    "ax.set_ylim([-0.02, 0.06])\n",
    "ax.set_yticks([-0.04, -0.02,  0, 0.02, 0.04, 0.06])\n",
    "ax.set_yticklabels([\"-4%\", \"-2%\",\"0%\",\"2%\", \"4%\", \"6%\"], fontsize=fs-2)\n",
    "ax.set_ylabel('welfare change (% of cons.)', fontsize=fs)\n",
    "\n",
    "if update_figs:\n",
    "    plt.savefig('fig2a.eps', bbox_inches='tight', format = 'eps', dpi = 100)\n",
    "plt.show()\n",
    "\n",
    "\n",
    "# plt.plot([p_opt, p_opt], [3.65, 3.8], \"--\");\n",
    "# plt.plot([p_SCPE, p_SCPE], [3.65, 3.8], \"--\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Incidence of the optimal progressivity reform"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "β0  =  1.082289236168935\n",
      "Var (log z|θ) =  0.2074460833577759\n",
      "Var (log c|θ) =  0.1391467423191451\n",
      "\n",
      " + crowd-out\n",
      "βco =  1.4210215711962826\n",
      "Δβco =  31.0 %\n",
      "Var (log y|θ) co =  0.35761843835809237 , % change:  172.0\n",
      "Var (log c|θ) co =  0.1391467423191451\n",
      "\n",
      " + crowd-in\n",
      "β1  =  1.1098002986265822\n",
      "Δβ1  =  3.0 %\n",
      "Var (log y|θ) =  0.20410857375143182 , % change:  98.0\n",
      "Var (log c|θ) final =  0.07941716665201703 % change: -42.925601183054006\n",
      "Offset rate:  0.9187822961884455\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 648x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Experiment: what happens to β when progressivity increases to the optimal level?\n",
    "\n",
    "# ε_pp, h̄_pp = params[3], params[4]\n",
    "# below l stands for π\n",
    "p0 = p_emp\n",
    "l0 = FindEffort(ε_pp, h̄_pp, p0, \"pp\")\n",
    "β0 = dh(l0, ε_pp, h̄_pp)/(1 - p0)\n",
    "\n",
    "p1 = p_opt\n",
    "# p1 = 2*p_emp\n",
    "βco = dh(l0, ε_pp, h̄_pp)/(1 - p1)\n",
    "l1 = FindEffort(ε_pp, h̄_pp, p1, \"pp\")\n",
    "β1 = dh(l1, ε_pp, h̄_pp)/(1 - p1)\n",
    "\n",
    "print(\"β0  = \", β0)\n",
    "print(\"Var (log z|θ) = \", l0*(1 - l0)*β0**2)\n",
    "print(\"Var (log c|θ) = \", (1 - p0)**2*l0*(1 - l0)*β0**2)\n",
    "\n",
    "print(\"\")\n",
    "print(\" + crowd-out\")\n",
    "print(\"βco = \", βco)\n",
    "print(\"Δβco = \", np.round(100*(βco - β0)/β0), \"%\")\n",
    "print(\"Var (log y|θ) co = \", l0*(1 - l0)*βco**2, \n",
    "      \", % change: \", np.round(100*(βco/β0)**2))\n",
    "print(\"Var (log c|θ) co = \", (1 - p1)**2*l0*(1 - l0)*βco**2)\n",
    "\n",
    "print(\"\")\n",
    "print(\" + crowd-in\")\n",
    "print(\"β1  = \", β1)\n",
    "print(\"Δβ1  = \", np.round(100*(β1 - β0)/β0), \"%\")\n",
    "print(\"Var (log y|θ) = \", l1*(1 - l1)*β1**2, \n",
    "      \", % change: \", np.round(100*(l1*(1 - l1)*β1**2)/(l0*(1 - l0)*β0**2)))\n",
    "print(\"Var (log c|θ) final = \", (1 - p1)**2*l1*(1 - l1)*β1**2, \"% change:\", 100*((1 - p1)**2*l1*(1 - l1)*β1**2/((1 - p0)**2*l0*(1 - l0)*β0**2) - 1))\n",
    "print(\"Offset rate: \", 1 - (β1 - β0)/(βco - β0))\n",
    "\n",
    "fs = 20\n",
    "Nbars = 3\n",
    "\n",
    "beta = np.array([β0, βco, β1])\n",
    "variance = np.array([l0*(1 - l0)*β0**2, l0*(1 - l0)*βco**2, l1*(1 - l1)*β1**2])\n",
    "\n",
    "fig, ax1 = plt.subplots(figsize=(9, 5))\n",
    "\n",
    "ax2 = ax1.twinx()\n",
    "\n",
    "var_aux = 1.038\n",
    "\n",
    "ax1.bar(np.arange(Nbars)-0.1, beta, 0.2, zorder=16, color=\"k\", label=\"$\\\\beta$\") # label=\"$\\\\beta$\"\n",
    "for i in range(Nbars):\n",
    "    ax1.annotate(str(np.round(beta[i], decimals=2)), (np.arange(Nbars)[i]-0.2, beta[i] + 0.005), fontsize=fs-3)\n",
    "\n",
    "ax2.bar(np.arange(Nbars)+0.1, variance, 0.2, zorder=15, edgecolor='k', fill=False, hatch='/', label=\"$Var(\\\\log \\\\ z | \\\\theta)$\");\n",
    "for i in range(Nbars):\n",
    "    if i==2:\n",
    "        ax2.annotate(str(np.round(variance[i], decimals=2)), (np.arange(Nbars)[i]+ 0.03, variance[i] + 0.003), fontsize=fs-3)\n",
    "    else:\n",
    "        ax2.annotate(str(np.round(variance[i], decimals=2)), (np.arange(Nbars)[i]+ 0.02, variance[i] + 0.003), fontsize=fs-3)\n",
    "\n",
    "        \n",
    "ax1.set_ylim([0.9, 1.5])\n",
    "ax2.set_ylim([0.15, 0.4])\n",
    "\n",
    "ax1.grid(which='major', axis='x', alpha = 0)\n",
    "ax2.grid(which='major', axis='x', alpha = 0)\n",
    "\n",
    "ax1.set_xticks(np.arange(3))\n",
    "ax1.set_xticklabels([ \"initial\", \"+ crowd-out\", \"+ crowd-in (final)\"], fontsize=fs)\n",
    "\n",
    "\n",
    "yticks1 = np.linspace(0.9, 1.5, 7)\n",
    "ax1.set_yticks(yticks1)\n",
    "ax1.set_yticklabels([str(y) for y in yticks1], fontsize=fs-4)\n",
    "\n",
    "yticks2 = np.linspace(0.15, 0.4, 6).round(decimals=2)\n",
    "ax2.set_yticks(yticks2)\n",
    "ax2.set_yticklabels([str(y) for y in yticks2], fontsize=fs-4)\n",
    "\n",
    "ax1.set_ylabel(\"bonus rate $\\\\beta$\", fontsize=fs, color=\"k\")\n",
    "ax2.set_ylabel(\"log earnings risk $Var(\\\\log \\\\ z | \\\\theta)$\", fontsize=fs, color=\"k\")\n",
    "\n",
    "ax1.grid(which='major', axis='y', alpha = 0)\n",
    "ax2.grid(which='major', axis='y', alpha = 0)\n",
    "\n",
    "ax1.set_xlim([-0.5, 2.5]);\n",
    "ax2.set_xlim([-0.5, 2.5]);\n",
    "\n",
    "ax1.legend(loc=\"upper left\", fontsize=fs-4, frameon=False)\n",
    "ax2.legend(loc=(0.02, 0.75), fontsize=fs-5, frameon=False)\n",
    "\n",
    "if update_figs:\n",
    "    plt.savefig('fig3.eps', bbox_inches='tight', format = 'eps', dpi = 100)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Additional figures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Share Q1:  0.36245359734298005\n",
      "Share Q2:  0.3900626429817068\n",
      "Share Q3:  0.44087819916110393\n",
      "Share Q4:  0.6066055605142091\n",
      "Share 75-90:  0.5463766057786872\n",
      "Share 90-95:  0.6598406223026108\n",
      "Share 95-100:  0.7340573629323731\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 648x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sig2_θ = σ2_pp\n",
    "θv = np.linspace(1, 10000, 2000)\n",
    "\n",
    "from scipy.stats import exponnorm\n",
    "\n",
    "K = (λ_θ *(sig2_θ)**0.5)**(-1)\n",
    "cdf_pp = exponnorm.cdf(np.log(θv), K, loc=μ_pp, scale=(sig2_θ)**0.5)\n",
    "\n",
    "# get rid of upper tail\n",
    "cdf_pp[-1] = 1\n",
    "\n",
    "# calculate density\n",
    "f_pp = np.hstack((np.diff(cdf_pp)/np.diff(θv), (np.diff(cdf_pp)/np.diff(θv))[-1]))\n",
    "\n",
    "K = (λ_θ *(sig2_θ)**0.5)**(-1)\n",
    "cdf_fp = exponnorm.cdf(np.log(θv), K, loc=μ_fp, scale=(sig2_θ)**0.5)\n",
    "cdf_fp[-1] = 1\n",
    "f_fp = np.hstack((np.diff(cdf_fp)/np.diff(θv), (np.diff(cdf_fp)/np.diff(θv))[-1]))\n",
    "\n",
    "# Produce figure\n",
    "l_fp = (1 - p_emp)**(ε/(1 + ε))    \n",
    "z_fp = θv * l_fp\n",
    "from scipy.interpolate import interp1d\n",
    "cdf_z_fp = interp1d(z_fp, cdf_fp)\n",
    "\n",
    "l_pp = FindEffort(ε_pp, h̄_pp, p_emp, \"pp\")\n",
    "β = dh(l_pp, ε_pp, h̄_pp)/(1 - p_emp)\n",
    "z_pp = θv*l_pp/(1 + l_pp*(np.exp(β) - 1))\n",
    "b_pp = z_pp*(np.exp(β) - 1)\n",
    "cdf_z_pp0 = np.cumsum(((1-l_pp)*f_pp)[:-1]*np.diff(θv))\n",
    "cdf_z_pp = interp1d(z_pp[:-1], cdf_z_pp0)\n",
    "\n",
    "cdf_zb_pp0 = np.cumsum((l_pp*f_pp)[:-1]*np.diff(θv))\n",
    "cdf_zb_pp = interp1d((z_pp + b_pp)[:-1], cdf_zb_pp0)\n",
    "                     \n",
    "def cdf_earnings(z):\n",
    "    return s_pp*(cdf_z_pp(z) + cdf_zb_pp(z)) + (1 - s_pp)*cdf_z_fp(z)\n",
    "                     \n",
    "y25 = brentq(lambda x: cdf_earnings(x) - 0.25, 10, 500)\n",
    "measure_ppQ1 = s_pp*(cdf_z_pp(y25) + cdf_zb_pp(y25))\n",
    "shareQ1 = measure_ppQ1/cdf_earnings(y25)\n",
    "print(\"Share Q1: \", shareQ1)\n",
    "\n",
    "y50 = brentq(lambda x: cdf_earnings(x) - 0.50, 10, 500)\n",
    "measure_ppQ2 = s_pp*(cdf_z_pp(y50) + cdf_zb_pp(y50)) - measure_ppQ1\n",
    "shareQ2 = measure_ppQ2/(cdf_earnings(y50) - cdf_earnings(y25))\n",
    "print(\"Share Q2: \", shareQ2)\n",
    "\n",
    "y75 = brentq(lambda x: cdf_earnings(x) - 0.75, 10, 500)\n",
    "measure_ppQ3 = s_pp*(cdf_z_pp(y75) + cdf_zb_pp(y75)) - measure_ppQ1 - measure_ppQ2\n",
    "shareQ3 = measure_ppQ3/(cdf_earnings(y75) - cdf_earnings(y50))\n",
    "print(\"Share Q3: \", shareQ3)\n",
    "\n",
    "measure_ppQ4 = s_pp - measure_ppQ1 - measure_ppQ2 - measure_ppQ3\n",
    "shareQ4 = measure_ppQ4/(1 - cdf_earnings(y75))\n",
    "print(\"Share Q4: \", shareQ4)\n",
    "\n",
    "y90 = brentq(lambda x: cdf_earnings(x) - 0.90, 10, 500)\n",
    "measure_pp75_90 = s_pp*(cdf_z_pp(y90) + cdf_zb_pp(y90)) - measure_ppQ1 - measure_ppQ2 - measure_ppQ3\n",
    "share75_90 = measure_pp75_90/(cdf_earnings(y90) - cdf_earnings(y75))\n",
    "print(\"Share 75-90: \", share75_90)\n",
    "\n",
    "y95 = brentq(lambda x: cdf_earnings(x) - 0.95, 10, 500)\n",
    "measure_pp90_95 = s_pp*(cdf_z_pp(y95) + cdf_zb_pp(y95)) - measure_ppQ1 - measure_ppQ2 - measure_ppQ3 - measure_pp75_90\n",
    "share90_95 = measure_pp90_95/(cdf_earnings(y95) - cdf_earnings(y90))\n",
    "print(\"Share 90-95: \", share90_95)\n",
    "\n",
    "measure_pp95_100 = s_pp - measure_ppQ1 - measure_ppQ2 - measure_ppQ3 - measure_pp75_90 - measure_pp90_95\n",
    "share95_100 = measure_pp95_100/(1 - cdf_earnings(y95))\n",
    "print(\"Share 95-100: \", share95_100)\n",
    "\n",
    "# share of performance pay jobs figure\n",
    "Nbars = 7\n",
    "percentiles = np.linspace(0, 1, Nbars + 1)\n",
    "\n",
    "shares_model = np.array([shareQ1, shareQ2, shareQ3, shareQ4, share75_90, share90_95, share95_100])\n",
    "shares_data = np.array([0.3761552, 0.4031590, 0.3707634, 0.6361486, \n",
    "                        0.5612454, 0.6072791, 0.8864745])\n",
    "\n",
    "fs = 20\n",
    "fig, ax = plt.subplots(figsize=(9, 5))\n",
    "\n",
    "# case = \"quartiles\" \n",
    "case = \"full\"\n",
    "\n",
    "ax.bar([x-0.15 for x in [0, 1, 2, 3]], 100*shares_data[:4], 0.3, label=\"data\", color=\"k\")\n",
    "ax.bar([x+0.15 for x in [0, 1, 2, 3]], 100*shares_model[:4], 0.3, label=\"model\", edgecolor='k', color=\"white\")\n",
    "\n",
    "if case == \"full\":\n",
    "    plt.gca().set_prop_cycle(None)\n",
    "    ax.bar([x-0.1 for x in [4, 4.75, 5.5]], 100*shares_data[4:], 0.2, color=\"k\")#, color=\"blue\")\n",
    "    ax.bar([x+0.1 for x in [4, 4.75, 5.5]], 100*shares_model[4:], 0.2, edgecolor='k', color=\"white\")#, color=\"orange\")\n",
    "\n",
    "ax.set_xlim([-0.3, 5.72])\n",
    "ax.set_xticks([0, 1, 2, 3])\n",
    "ax.set_xticklabels([ \"0-25\", \"25-50\", \"50-75\", \"75-100\"], fontsize=fs-2)\n",
    "\n",
    "if case == \"full\":\n",
    "    ax.set_xticks([0, 1, 2, 3, 4, 4.75, 5.5])\n",
    "    ax.set_xticklabels([ \"0-25\", \"25-50\", \"50-75\", \"75-100\",\"75-90\", \"90-95\", \"95-100\"], fontsize=fs-2)\n",
    "ax.grid(which='major', axis='x', alpha = 0)\n",
    "ax.set_xlabel(\"earnings percentiles\", fontsize=fs)\n",
    "\n",
    "ax.set_ylim([0, 100])\n",
    "ax.set_yticks(np.linspace(0, 100, 6))\n",
    "ax.set_ylabel(\"share of perf.-pay jobs (%)\", fontsize=fs)\n",
    "ax.set_yticklabels([\"0\", \"20\", \"40\", \"60\", \"80\", \"100\"], fontsize=fs-2)\n",
    "plt.legend(fontsize=fs, loc=\"upper left\");\n",
    "\n",
    "if update_figs:\n",
    "    if case == \"quartiles\":\n",
    "        plt.savefig('figures/share-ppjobs-earnings-quartiles.eps', bbox_inches='tight', format = 'eps', dpi = 100)    \n",
    "    if case == \"full\":\n",
    "        plt.savefig('fig1b.eps', bbox_inches='tight', format = 'eps', dpi = 100)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "The PostScript backend does not support transparency; partially transparent artists will be rendered opaque.\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 648x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# graph with log hourly earnings (compare to figure 3 LMP)\n",
    "\n",
    "from scipy.stats import exponnorm\n",
    "\n",
    "# fix-pay jobs\n",
    "logwrV = np.linspace(1.5, 7.5, 1000)\n",
    "K_fp = 1 / (λ_θ*sig2_θ**0.5)\n",
    "pdf_fp = exponnorm.pdf(logwrV, K_fp, loc=μ_fp + np.log(l_fp), scale=sig2_θ**0.5)\n",
    "cdf_fp = exponnorm.cdf(logwrV, K_fp, loc=μ_fp + np.log(l_fp), scale=sig2_θ**0.5)\n",
    "\n",
    "# performance-pay jobs\n",
    "w_base1 = l_pp/(l_pp*np.exp(β) + 1 - l_pp)\n",
    "K_pp = 1 / (λ_θ*sig2_θ**0.5)\n",
    "\n",
    "pdf_pp_base = exponnorm.pdf(logwrV, K_pp, loc=μ_pp + np.log(w_base1), scale=sig2_θ**0.5)\n",
    "cdf_pp_base = exponnorm.cdf(logwrV, K_pp, loc=μ_pp + np.log(w_base1), scale=sig2_θ**0.5)\n",
    "\n",
    "pdf_pp_bonus = exponnorm.pdf(logwrV, K_pp, loc=μ_pp + np.log(w_base1) + β, scale=sig2_θ**0.5)\n",
    "cdf_pp_bonus = exponnorm.cdf(logwrV, K_pp, loc=μ_pp + np.log(w_base1) + β, scale=sig2_θ**0.5)\n",
    "\n",
    "pdf_pp = l_pp * pdf_pp_bonus + (1 - l_pp)*pdf_pp_base\n",
    "cdf_pp = l_pp * cdf_pp_bonus + (1 - l_pp)*cdf_pp_base\n",
    "\n",
    "# log-wage density plot\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(9, 5))\n",
    "ax.plot(logwrV, pdf_fp, \"--\", lw=3, label=\"fix-pay jobs\", c=\"k\")\n",
    "ax.plot(logwrV, pdf_pp, lw=3, label=\"perf.-pay jobs\", c=\"k\")\n",
    "\n",
    "fs = 20\n",
    "ax.set_xlabel(\"log earnings\", fontsize=fs)\n",
    "ax.set_ylabel(\"density\", fontsize=fs)\n",
    "\n",
    "xticks = np.array([2, 3, 4, 5, 6, 7])\n",
    "ax.set_xticks(xticks)\n",
    "ax.set_xticklabels([str(x) for x in xticks], fontsize=fs-2)\n",
    "\n",
    "yticks = np.array([0, 0.2, 0.4, 0.6])\n",
    "ax.set_yticks(yticks)\n",
    "ax.set_yticklabels([str(y) for y in yticks], fontsize=fs-2)\n",
    "\n",
    "ax.set_xlim([logwrV[0], logwrV[-1]])\n",
    "ax.set_ylim([0, 0.7])\n",
    "plt.legend(fontsize=fs, loc=\"best\");\n",
    "\n",
    "if update_figs:\n",
    "    plt.savefig('fig1a.eps', bbox_inches='tight', format = 'eps', dpi = 100)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
